First ANDES annual meeting

Transcription

1 First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 1 / 0 *C.J. Díez cj.diez@upm.es carlosjavier@denim.upm.es UNCERTAINTY METHODS IN ACTIVATION AND INVENTORY CALCULATIONS Carlos J. Díez*, O. Cabellos, J.S. Martínez Universidad Politécnica de Madrid (UPM) First ANDES annual meeting CIEMAT, Madrid (Spain), May 3 5, 011

2 Task.4 Covariances for activation, radioactive decay and fission yields Task leader: UPM Participants: UPM, NRG, NNL, CIEMAT For a number of important nuclides, complete activation data libraries with covariance data will be produced, so that uncertainty propagation in fuel cycle codes (in this case ACAB, FISPIN,...) can be developed and tested. Eventually, fuel inventory codes should be able to handle the complete set of uncertainty data, i.e. those of nuclear reactions (cross sections, etc.), radioactive decay and fission yield data. For this, capabilities will be developed both to produce covariance data and to propagate the uncertainties through the inventory calculations. Demonstrations on a realistic burn-up case will be provided. First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain / 0

3 Deliverables and Milestones Milestones: M.. Report on the usability of Monte Carlo uncertainty propagation in fuel cycle codes, and comparison with conventional approach (31 May 01) (UPM/UNED, NRG, CIEMAT). M.3. An upgraded ACAB code, which now will deal with cross-channel and cross-nuclide correlations (31 May 01) (UPM) M.4. New computational method for the use of covariance information of reaction, decay and fission yield data in an inventory calculation (31 May 01)(NNL) Deliverables: D.1. Activation data libraries for Monte Carlo uncertainty propagation in fuel cycle code ACAB (31 May 011) (UPM) by the end of June 011 (according to the schedule ) D.5. Report with transmutation calculations for advanced reactors with new covariance data + updated sensitivity tables. (31 May 013) (NNL) D.6. Report on the impact of uncertainties of the fission product nuclear data on the inventory of the irradiated fuel for ACAB (31 May 013) (UPM) First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 3 / 0

4 Abstract ACTIVATION CALCULATIONS Different error propagation techniques can be used: Sensitivity analysis Response Surface Method Monte Carlo technique Then, in this paper, it is assessed the impact of ND uncertainties on response functions in two applications: Fission Pulse Decay Heat calculation (FPDH) (in collaboration with R. Mills) Conceptual design of European Facility for Industrial Transmutation (EFIT) The complete set of uncertainty data for cross sections (EAF007/UN), decay data and fission yield data (JEFF-3.1.1) are processed and used in ACAB code. First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 4 / 0

5 PART I Methodology to propagate ND uncertainties dn dt Goal: To analyse how ND uncertainties are transmitted to response functions [ ] [ ] [ ] eff eff N + σ ΦN + (γσ ΦN = A N λ N = ( λ, σ, γ ) = ) ) Monte Carlo Uncertainty Analysis (MC) To treat the global effect of all nuclear data uncertainties Without any approximation fiss i N i Nuclear Data libraries Collapsed Mean Values Uncertainties (Standard Desv) LogNormal distribution λ, γ, σ Samplig λ, γ, σ 1 λ, γ, σ... λ, γ, σ n 1 n 1 n ACAB Results N N... 1 N n First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 5 / 0

6 PART I Methodology to propagate ND uncertainties Uncertainty data Cross section from activation-oriented nuclear data libraries EAF007-UN E i+1 (ev) e.g.: W 180 (n,γ) W -180N,G E E E+00 00E E+00 00E E E E E E E E E E+07 00E I=1,EAF E i (ev) Fission yield from evaluated nuclear data library Th3 400 KeV H3 JEFF (relative error, )~ I=1,EXP = I=1,EAF /3 γ Th H 3,400KeV 1σ γ E+05 00E E+03 00E E E E+03 00E E E E+03 00E E E First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 6 / 0.

7 PART I Methodology to propagate ND uncertainties Processing and collapsing of nuclear data Collapsing method: -Cross section: Conservation of reaction rate Rate j eff i = σ j i ( E) φ( E de = σ j i E ) φ T -Uncertainties: Using Sandwich rule (Propagation of Momentum, first order) = ω T Vω. Cross section ω = φ σ φ σ φ σ φ σ 1 1 G G T [,, ] eff eff Fission yield φ σ 1 1, fiss φ σ G ω = [,, eff φ σ φ σ fiss G, fiss eff fiss ] T First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 7 / 0 7

8 PART I Methodology to propagate ND uncertainties Advantages & Disadvantages of Monte Carlo Technique Advantages Collapsing to one energy group Reduce amount of variables to sample No sensitivity coefficients should be calculated No approximation on equations Take into account non-linear effects Disadvantages How to check if the phase space is well sampled? Which PDFs should be taken? Computational demanding Monte Carlo Technique & Sensitivity Analysis are compatible First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 8 / 0

9 APPLICATIONS APPLICATIONS: A. Fission Pulse Decay Heat calculation First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 9 / 0

10 APPLICATIONS First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 10 / 0

11 Reference system One of the preliminary conceptual designs of the European Facility for Industrial Transmutation (EFIT) Coolant Thermal Power Fuel Initial mass of actinides Pure Lead 400 MWth (Pu, Am)O + MgO.074 tonnes 1,E-03 Constant neutron environment: - neutron flux: 3.1 x n/cm s - average energy <E> = 0.37 MeV Calculations for discharge burn-up: GWd/tHM (778 irradiation days) GWd/tHM (35 irradiation days) Normalized Neutron Flux 1,E-04 1,E-05 1,E-06 1,E-07 Initial 400 days Initial total flux intensity =.84E+15 n cm - s days total flux intensity = 3.1E+15 n cm - s -1 1,E-08 1,E-09 1,E-06 1,E-05 1,E-04 1,E-03 1,E-0 1,E-01 1,E+00 1,E+01 1,E+0 Eneutron (MeV) First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 11 / 0

12 Calculations Histories launched: 1000/DH case 300/RTX case Case studied 1. Decay heat. Radiotoxicity a.inhalation dose b.ingestion dose relative error per each time step (%) Number of histories All uncertainties are propagated: - Individually - All together σ, γ, λ ~300 First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 1 / 0

13 Decay heat for 150 GWd/tHM DH Ref DH M-C Error XS+FY+Decay Error XS Error FY Error Decay 1.00E E E+06 5 Decay Heat (W) 1.00E E E Error (%) 1.00E E E E-0 1.0E E E E+0 1.0E E E E+06 Cooling Time (years) First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 13 / 0

14 Decay heat for 150 GWd/tHM var( y) = DH total = DH i N i= 1 var( y ) + i i= isotope N i, j= 1; i j Main contributors analysis cov( y, y ) i j N i= 1 σ x x var( y ) >> = N i i= 1 σ y yi i N i, j= 1; i j y x i cov( y, y ) = N i= 1 i j error( y ) i y x i var(i)/var( ) cov(i,j)/var( ) E E-0 1.0E E E E+0 1.0E E E E+06 Cooling Time (years) First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 14 / 0 14

15 Decay heat for 150 GWd/tHM Main contributors Cm4 Cm44 Pu38 Am41 Pu40 Pu39 TOTAL CM4 CM44 PU38 AM41 PU40 PU39 PO14 PO error (%) E E-0 1.0E E E E+0 1.0E E E E+06 Cooling Time (years) First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 15 / 0

16 Radiotoxicity for 150 GWd/tHM Ingestion Xe133 Cm44 Pu38 Am41 Rn Due to FY / XS error Ingestion error (%) Ingestion error (%) Error XS+FY+DECAY Error XS Error FY Error DECAY E E-0 1.0E E E E+0 1.0E E E E+06 Cooling time (years) TOTAL XE133 CM44 PU38 AM41 RN E E-0 1.0E E E E+0 1.0E E E E+06 Cooling time (years) First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 16 / 0

17 Differences between 150 GWd/tHM and 500 GWd/tHM Error varation because of burn-up discharge Decay Heat Inhalation dose Ingestion dose 150 GWd/tHM 6.67% 3.70% 4.33% 500 GWd/tHM 9.83% 9.04% 9.45% t burn-up => error Main contributors in each burn-up discharge Xe133 Rn Pu38 Pu39 Pu40 Am41 Cm4 Cm GWd/tHM Ing Inh, Ing DH, Inh, Ing DH DH, Inh DH, Inh, Ing DH DH, Inh, Ing 500 GWd/tHM Ing Inh, Ing DH, Inh, Ing DH DH, Inh DH, Inh, Ing - DH, Inh, Ing First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 17 / 0

18 CONCLUSIONS First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 18 / 0

19 CONCLUSIONS Monte Carlo technique for ND uncertainty propagation in activation calculations Pre-proccesing of nuclear data is needed: Implemented on ACAB code - Identifying uncertainties - PDFs selection - Collapsing of nuclear data Monte Carlo technique VS deterministic calculations / experimental data A good agreement is found between both PDFs dependence is found in FPDH calculation, but not in EFIT calculation A method to identify main contributors to error is developed based on MC results Importance of fission yield uncertainties depends on the applications and which response functions is studied First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 19 / 0

20 First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 0 / 0 C.J. Díez cj.diez@upm.es carlosjavier@denim.upm.es THANK YOU FOR YOUR ATTENTION!!

21 Radiotoxicity for 150 GWd/tHM Inhalation Cm44 Pu38 Am41 Pu40 Rn Inhalation error (%) Inhalation error (%) Error XS+FY+DECAY Error XS Error FY Error DECAY E E-0 1.0E E E E+0 1.0E E E E+06 Cooling time (years) TOTAL CM44 PU38 AM41 PU40 RN E E-0 1.0E E E E+0 1.0E E E E+06 Cooling time (years) First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 1 / 0

22 Decay heat for 500 GWd/tHM DH Ref DH M-C Error XS+FY+Decay Error XS Error FY Error Decay 1.0E E+06 8 Decay Heat (W) 1.0E E Error (%) 1.0E E E E-0 1.0E E E E+0 1.0E E E E+06 Cooling Time (years) First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain / 0

23 Decay heat for 500 GWd/tHM TOTAL CM44 PU38 AM41 PU40 PU39 PO14 PO13 error (%) Cm44 Pu38 Am41 Pu40 Pu39 1.0E E-0 1.0E E E E+0 1.0E E E E+06 Cooling Time (years) 1.40 var(i)/var( ) cov(i,j)/var( ) E E-0 1.0E E E E+0 1.0E E E E+06 Cooling Time (years) First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 3 / 0 3

24 Radiotoxicity for 500 GWd/tHM Inhalation var(i)/var( ) cov(i,j)/var( ) 1.0E E-0 1.0E E E E+0 1.0E E E E+06 Cooling time (years) TOTAL CM44 PU38 AM41 PU40 RN Cm44 Pu38 Am41 Pu40 Rn Error (%) E E-0 1.0E E E E+0 1.0E E E E+06 Cooling time First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 4 / 0

25 Radiotoxicity for 500 GWd/tHM Ingestion var(i)/var( ) cov(i,j)/var( ) 1.0E E-0 1.0E E E E+0 1.0E E E E+06 Cooling time TOTAL XE133 CM44 PU38 AM41 RN Xe133 Cm44 Pu38 Am41 Rn error (%) E E-0 1.0E E E E+0 1.0E E E E+06 Cooling time (years) First ANDES Annual meeting 3-5 May 011 CIEMAT, Madrid, Spain 5 / 0